Topological Structures of Function Spaces是一本深入研究函數(shù)空間的拓撲結構的全新專著。它系統(tǒng)性地總結了過去二十年來（包括作者和其他學者）的相關研究成果，是當前拓撲學研究的重要資料。此書中涵蓋的內(nèi)容不僅適合拓撲學的學術研究者使用，也對應用數(shù)學和相關領域的學者有重要參考價值。
作者簡介
楊忠強，閩南師范大學二級教授，博士生導師。1990年和1994年分別在四川大學數(shù)學系和日本筑波大學數(shù)學研究所取得理學博士學位和博士（數(shù)學）學位。1989年“格與拓撲”獲陜西省政府科技進步一等獎，4次主持國家自然科學面上項目，4次主持省部級自然科學面上項目，2次獲得中國國家留學基金委資助赴外研究。研究領域為無限維拓撲學，一般拓撲學，拓撲動力系統(tǒng)，統(tǒng)計學，模糊數(shù)學，格上拓撲學，格論等。 楊寒彪，五邑大學副教授，碩士導師，獲得日本筑波大學博士學位，主要從事主要研究無限維拓撲學函數(shù)空間的研究。主持過國家自然科學基金青年項目1項，天元項目1項目，廣東省自然科學基金面上項目1項和博士啟動項目1項目，近年來在Topology and its Applications、Open Mathematics等國際數(shù)學期刊上發(fā)表近十篇論文。 鄔恩信，汕頭大學副教授，碩士生導師。2012年畢業(yè)于加拿大西安大略大學。主持1項國家自然科學青年基金，參加1項國家自然科學基金面上項目。研究領域為拓撲學和幾何學，目前主要研究廣義流形（diffeology）相關的幾何與拓撲及其應用。
圖書目錄
Contents Preface by J. van Mill iii
Preface v
Overview 1
1 Basic Theory 7 1.1 Preliminaries 7 1.2 Several theorems in general topology 14 1.3 ARs and ANRs 24 1.4 Z-sets and strong Z-sets 34 1.5 Homotopy denseness and SDAP 38 1.6 Absorbing sets and coabsorbing sets 42 1.7 Characterizations for some classical spaces 53 Note for Chapter 1 58
2 Topological Structures of Hyperspaces 61 2.1 Hyperspaces 61 2.2 Hyperspace theorem for Vietoris topology 67 2.3 Hyperspace theorem for Fell topology 71 2.4 Supplements and problems about hyperspaces 76 Note for Chapter 2 79
3 Function Spaces with Endograph Fell Topology 81 3.1 Properties of function spaces with Endograph Fell topology 81 3.2 Conditions for being metrizable of USC(X,I) 93 3.3 Conditions for being metrizable of continuous function spaces 97 3.4 A compacti?cation of metrizable continuous function space 106 3.5 Borel complexity and Baire property of space of continuous functions 111 3.6 Strong universality of continuous function space, I 121 3.7 Strong universality of continuous function space, II 132 3.8 Topological structures of function spaces 141 3.9 Remarks and problems about continuous maps 142 3.10 Appendix: Baire property 145 Note for Chapter 3 151
4 Topological Structures of Spaces of Fuzzy Numbers 153 4.1 Metrics on set of fuzzy numbers 154 4.2 Compactness and completeness of spaces of fuzzy numbers 160 4.3 Spaces of fuzzy numbers are ARs 167 4.4 Topological structures with endograph metric and Lp metrics 176 4.5 Topological structures with sendograph metric and L∞ metrics, I 186 4.6 Topological structures with sendograph metric and L∞ metrics, II 192 4.7 Remarks and problems about fuzzy numbers 201 Note for Chapter 4 204
5 Function Spaces Coming from Probability Theory 207 5.1 Spaces of copulas and subcopulas 207 5.2 Spaces of copulas and exchange copulas 216 5.3 Topological structure of space of subcouplas 221 5.4 Remarks and problems about spaces of copulas 226 Note for Chapter 5 230
6 Function Spaces Coming from Dynamical Systems 233 6.1 Box maps on closed intervals 233 6.2 Function spaces related to topological entropy 239 6.3 Topological structures of function spaces of transitive maps 251 6.4 Remarks and problems about spaces related to dynamical systems 261 Note for Chapter 6 263
7 Function Spaces Coming from Metric Measure Spaces 265 7.1 Basic knowledge on metric measure spaces 265 7.2 Topological structures of spaces of uniformly continuous functions 267 7.3 Pair of spaces on metric measure spaces 275 7.4 Remarks and problems about metric measure spaces 281 Note for Chapter 7 281
鄂公網(wǎng)安備 42010302001612號 